what are the brand and model of your AC and and how do you get this data (processor/board, IR library used, ...) ? It seems you have something wrong as you don't have full bytes. When I try to split in bytes I have 3 bits alone at the end so you are missing data somewhere.

Usually the checksum is just a xor. It doesn't seem to be the case for yours, but maybe it's because you are missing some data.

@Nca78 Thanks for the answer.
The brand of the AC is a local brand called "Tadiran" (not sure if its world distributed).
I am capturing the IR code with following arduino code, please note you need this code because AC have very long IR code since every button push the whole state is sent i.e. fan speed temp mode etc.
Now i know that the code i am capturing is good because i can successfully transmit it back using any IR library.

I agree on the uneven bytes and could not figure this out as well, i also tried the XOR checksum and couldn't get it to match.
The output i am getting from the code is of time delays which i later convert to binary i use the follow mapping to convert to bin:
HDR_MARK 9000
HDR_SPACE 4000
BIT_MARK 620
ONE_SPACE 1600
ZERO_SPACE 540
MSG_SPACE 19000

Please note that there is a message space of around 19 ms that separates the message in to 2 parts, the second part does not change beside the last 4 digits which i think is the checksum. the long pause is right after the 3 digits, so for an example look at the code i got below for a certain operation, they all got the same checksum:
cold, 26 C
Fan:
Auto
100100000101000000000110000 0101001000000000000001000000000000001111
Fan1
100110000101000000000110000 0101001000000000000001000000000000001111
Fan2
100101000101000000000110000 0101001000000000000001000000000000001111
Fan3
100111000101000000000110000 0101001000000000000001000000000000001111

I appreciate the help and hope we can resolve this as i am about to give up...

From wikipedia :
"Tadiran Appliances (also known as Tadiran Air Conditioners), was acquired by the Carrier Corporation, the world’s largest manufacturer and distributor of heating, ventilating and air conditioning (HVAC) systems, itself a subsidiary of United Technologies Corporation (UTC) of the USA and a constitute of Dow Jones Industrial Average. Carrier initially acquired 26%of the company in 1997 and took full ownership of it in 2004.[2]"

So looking for Carrier AC infrared should probably help.
Is the reference of your remote control (on the sticker at the back) YB1FA ? As it seems to be shared by gree/carrier/tadiran/ferroli/condor

Now we just need to understand what bits are included or not in the sum, it seems the fan speed is not, but we need more messages in different modes and with different settings to be able to know which bits are used or not in the calculation.

Invert bit order and try to guess what words are included or not.
If you make the sum of included words with binary calculator, it matches the checksum but we must validate with more parameters changed, try with horizontal/vertical swing if you have these on the remote control, then any other specific function.

1001 => on + mode, included as it's the only one with LSB = 1 and we have LSB = 1 in checksum
0000 => fan speed, not included as shown in your examples on fan speed
1010 => temp 16°C + value, included as shown in your examples of temperature
0000 => ??? cannot know because 0
0000 => ??? cannot know because 0
0110 => I think included else I don't have the right checksum
000 19 ms space => I ignore this part as it's not matching the 4 bits words, and only 0s anyway
1010 => I think not included else I don't have the right checksum
0100 => I think included else I don't have the right checksum
0000 => ??? cannot know because 0
0000 => ??? cannot know because 0
0000 => ??? cannot know because 0
0100 => I think included else I don't have the right checksum
0000 => ??? cannot know because 0
0000 => ??? cannot know because 0
0000 => ??? cannot know because 0
1111 => binary sum of all included words, only the 4 LSB bits are kept

@dpressle
I add it because it is the initial value of the checksum when temperature is 16°C = 0000
I just wanted to show than an increase of 1 in temperature was producing an increase of 1 in checksum.

I think your minus sign (= 19ms pause ?) is in wrong position as it is supposed to be after the 6 (and not 8 ) first words ?

Please take some values by changing the horizontal and vertical swing so we can try to change the second part of the message. After that try some other functions if you have (anything like "eco"/"quiet"/"turbo" options for example) and also if you have it the timer.

@dpressle could you please also post a picture of the back of your remote control ? I would like to confirm it's the one I quoted above, would be very interesting as it seems this RC/protocol is shared with a loooot of brands and models.
It's a very interesting case for this reason but also because it's using a checksum based on 4 bits words and excluding some of the "data" bits (at least the fan speed), it's the first time I see this.

@Nca78 Unfortunately not. This is a part of the document which we use to define IR codes for our product called PebbleAIR . These codes are implemented in the Android and iOS app. It took me a lot of time, money and effort to decode all the different brands and remotes. I often browse the forums and if I see that someone is stuck or in a need, I share remote data from time to time. If you desperately need data for a certain brand od model feel free to PM me, and I might help you.

@joker_mkd product looks great, did you ever thought of making these units smaller (so can be attached on an AC for example) and have some kind of API exposed so any Home Automation can use them? MySensors ZWave Wifi http etc...

@dpressle We are in the process of making an API, because several companies have asked us for this. I was not involved in the process of hardware design, and I agree that the unit could have been made smaller, probably in the next revision.